Is Blender the right software to make 3D animations of Mechanical components and assembly?
If you are looking for an actual force driven physics based simulation, Blender can be limited in that area and is probably not adequate for what you are seeking.

Bullet, the physics engine behind Blender is quite capable but not very suited for mechanical workings, and tight fittings and chained interactions like mechanical parts do not work well there and glitch out very easily.

On the other hand, if you don't mind a geometry/maths based solution, then Blender it sounds right for you, and Blender should be perfectly able to do what you see in the video. If you are looking for illustrations of mechanical parts and animations of simulations the constrains system should be quite adequate and easy to set up.

You may want to look into constraints based animations tutorials
See:


Precise Mechanical Rigging (Intuitive method)
How to animate winding a ribbon onto a cylinder?
Rigging an umbrella-like object
Is Blender a sensible environment for making a first-person orrery?